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EstimatedPointProcess
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EstimatedPointProcess

[Experimental]

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EstimatedPointProcess[pdata,pproc]

estimates the parametric point process pproc from point data pdata.

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EstimatedPointProcess[pdata,pproc,{{p,p0},{q,q0},…}]

estimates the parameters p, q, … with starting values p0, q0, ….

Details and Options

  • EstimatedPointProcess takes point data pdata and returns the symbolic point process pproc with parameter estimates inserted for any non-numeric values.
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  • In general, a process pproc can be better estimated from an ensemble of point data.
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  • The points pdata can have the following forms:
  • {p1,p2,…}points pi
    GeoPosition[…],GeoPositionXYZ[…],…geographic points
    SpatialPointData[…]spatial point collection
    {pts,reg}point collection pts and observation region reg
  • The points are converted to a SpatialPointData object and a Ripley–Rasson estimator is used to generate the observation region if it is not provided in pdata.
  • The following options can be given:
  • AccuracyGoalAutomaticthe accuracy sought
    PointProcessEstimator Automaticwhat process parameter estimator to use
    PrecisionGoalAutomaticthe precision sought
    WorkingPrecision Automaticthe precision used in internal computations
  • Settings for PointProcessEstimator are documented under the individual point process reference pages.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Estimate the parameter of a PoissonPointProcess:

In[1]:=1
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https://wolfram.com/xid/0rkj1dix01g16ya-87m94z
In[2]:=2
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https://wolfram.com/xid/0rkj1dix01g16ya-ntrd4p
Out[2]=2

Compare the nearest neighbor function of the estimated process to the original data:

In[3]:=3
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https://wolfram.com/xid/0rkj1dix01g16ya-hb971p
In[5]:=5
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https://wolfram.com/xid/0rkj1dix01g16ya-ijidg5
Out[5]=5

Scope  (3)Survey of the scope of standard use cases

Cluster point processes  (1)

Simulate a point configuration from a Matern point process:

In[1]:=1
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https://wolfram.com/xid/0rkj1dix01g16ya-8c7zax
In[2]:=2
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https://wolfram.com/xid/0rkj1dix01g16ya-9g5xhe
Out[2]=2

Use the "FindClusters" method to estimate a point process model:

In[3]:=3
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https://wolfram.com/xid/0rkj1dix01g16ya-3o7emz
Out[3]=3

Compare the Ripley measure between the original process and the estimated model:

In[4]:=4
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https://wolfram.com/xid/0rkj1dix01g16ya-m5qyr2
Out[4]=4

Gibbs point processes  (2)

Estimate a hardcore point process:

In[1]:=1
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https://wolfram.com/xid/0rkj1dix01g16ya-f65qge
In[2]:=2
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https://wolfram.com/xid/0rkj1dix01g16ya-v1my3r
Out[2]=2

Use automatic method:

In[3]:=3
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https://wolfram.com/xid/0rkj1dix01g16ya-0lrhw4
Out[3]=3

Estimate an interaction point process:

In[1]:=1
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https://wolfram.com/xid/0rkj1dix01g16ya-m3vtqd
In[2]:=2
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https://wolfram.com/xid/0rkj1dix01g16ya-02lrvk
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0rkj1dix01g16ya-ktpc3y
Out[3]=3

Estimate the point process:

In[4]:=4
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https://wolfram.com/xid/0rkj1dix01g16ya-g1jfw2
Out[4]=4

Options  (3)Common values & functionality for each option

PointProcessEstimator  (2)

Estimate a cluster point process:

In[1]:=1
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https://wolfram.com/xid/0rkj1dix01g16ya-3xtnqr

Use the "FindClusters" method to estimate a point process model:

In[3]:=3
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https://wolfram.com/xid/0rkj1dix01g16ya-qqtrbj
Out[3]=3

Use the method of moments:

In[4]:=4
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https://wolfram.com/xid/0rkj1dix01g16ya-qlcixz
Out[4]=4

Estimate an interaction process:

In[1]:=1
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https://wolfram.com/xid/0rkj1dix01g16ya-k4hl1s

Use "MaximumPseudoLikelihood" method:

In[2]:=2
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https://wolfram.com/xid/0rkj1dix01g16ya-gtlp8y
Out[2]=2

Use "MaximumLikelihood" method:

In[3]:=3
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https://wolfram.com/xid/0rkj1dix01g16ya-knkvty
Out[3]=3

WorkingPrecision  (1)

Estimate a cluster point process with arbitrary precision:

In[1]:=1
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https://wolfram.com/xid/0rkj1dix01g16ya-60qt3t

Specify WorkingPrecision:

In[3]:=3
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https://wolfram.com/xid/0rkj1dix01g16ya-v0w81j
Out[3]=3

EstimatedPointProcess uses MachinePrecision as default:

In[4]:=4
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https://wolfram.com/xid/0rkj1dix01g16ya-0s6dcu
Out[4]=4
Wolfram Research (2020), EstimatedPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/EstimatedPointProcess.html.
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Wolfram Research (2020), EstimatedPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/EstimatedPointProcess.html.

Text

Wolfram Research (2020), EstimatedPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/EstimatedPointProcess.html.

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Wolfram Research (2020), EstimatedPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/EstimatedPointProcess.html.

CMS

Wolfram Language. 2020. "EstimatedPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EstimatedPointProcess.html.

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Wolfram Language. 2020. "EstimatedPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EstimatedPointProcess.html.

APA

Wolfram Language. (2020). EstimatedPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EstimatedPointProcess.html

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Wolfram Language. (2020). EstimatedPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EstimatedPointProcess.html

BibTeX

@misc{reference.wolfram_2025_estimatedpointprocess, author="Wolfram Research", title="{EstimatedPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/EstimatedPointProcess.html}", note=[Accessed: 02-June-2025 ]}

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@misc{reference.wolfram_2025_estimatedpointprocess, author="Wolfram Research", title="{EstimatedPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/EstimatedPointProcess.html}", note=[Accessed: 02-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_estimatedpointprocess, organization={Wolfram Research}, title={EstimatedPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/EstimatedPointProcess.html}, note=[Accessed: 02-June-2025 ]}

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@online{reference.wolfram_2025_estimatedpointprocess, organization={Wolfram Research}, title={EstimatedPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/EstimatedPointProcess.html}, note=[Accessed: 02-June-2025 ]}